code: def bit_flip_mixer(graph: Union[nx.Graph, rx.PyGraph], b: int):
      r"""Creates a bit-flip mixer Hamiltonian.
  
      This mixer is defined as:
  
      .. math:: H_M \ = \ \displaystyle\sum_{v \in V(G)} \frac{1}{2^{d(v)}} X_{v}
                \displaystyle\prod_{w \in N(v)} (\mathbb{I} \ + \ (-1)^b Z_w)
  
      where :math:`V(G)` is the set of vertices of some graph :math:`G`, :math:`d(v)` is the
      `degree <https://en.wikipedia.org/wiki/Degree_(graph_theory)>`__ of vertex :math:`v`, and
      :math:`N(v)` is the `neighbourhood <https://en.wikipedia.org/wiki/Neighbourhood_(graph_theory)>`__
      of vertex :math:`v`. In addition, :math:`Z_v` and :math:`X_v`
      are the Pauli-Z and Pauli-X operators on vertex :math:`v`, respectively,
      and :math:`\mathbb{I}` is the identity operator.
  
      This mixer was introduced in `Hadfield et al. (2019) <https://doi.org/10.3390/a12020034>`__.
  
      Args:
           graph (nx.Graph or rx.PyGraph): A graph defining the collections of wires on which the Hamiltonian acts.
           b (int): Either :math:`0` or :math:`1`. When :math:`b=0`, a bit flip is performed on
               vertex :math:`v` only when all neighbouring nodes are in state :math:`|0\rangle`.
               Alternatively, for :math:`b=1`, a bit flip is performed only when all the neighbours of
               :math:`v` are in the state :math:`|1\rangle`.
  
      Returns:
          Hamiltonian: Mixer Hamiltonian
  
      **Example**
  
      The mixer Hamiltonian can be called as follows:
  
      >>> from pennylane import qaoa
      >>> from networkx import Graph
      >>> graph = Graph([(0, 1), (1, 2)])
      >>> mixer_h = qaoa.bit_flip_mixer(graph, 0)
      >>> print(mixer_h)
        (0.25) [X1]
      + (0.5) [X0]
      + (0.5) [X2]
      + (0.25) [X1 Z2]
      + (0.25) [X1 Z0]
      + (0.5) [X0 Z1]
      + (0.5) [X2 Z1]
      + (0.25) [X1 Z0 Z2]
  
      >>> import rustworkx as rx
      >>> graph = rx.PyGraph()
      >>> graph.add_nodes_from([0, 1, 2])
      >>> graph.add_edges_from([(0, 1, ""), (1, 2, "")])
      >>> mixer_h = qaoa.bit_flip_mixer(graph, 0)
      >>> print(mixer_h)
        (0.25) [X1]
      + (0.5) [X0]
      + (0.5) [X2]
      + (0.25) [X1 Z0]
      + (0.25) [X1 Z2]
      + (0.5) [X0 Z1]
      + (0.5) [X2 Z1]
      + (0.25) [X1 Z2 Z0]
      """
  
      if not isinstance(graph, (nx.Graph, rx.PyGraph)):
          raise ValueError(
              f"Input graph must be a nx.Graph or rx.PyGraph object, got {type(graph).__name__}"
          )
  
      if b not in [0, 1]:
          raise ValueError(f"'b' must be either 0 or 1, got {b}")
  
      sign = 1 if b == 0 else -1
  
      coeffs = []
      terms = []
  
      is_rx = isinstance(graph, rx.PyGraph)
      graph_nodes = graph.node_indexes() if is_rx else graph.nodes
  
      # In RX each node is assigned to an integer index starting from 0;
      # thus, we use the following lambda function to get node-values.
      get_nvalue = lambda i: graph.nodes()[i] if is_rx else i
  
      for i in graph_nodes:
          neighbours = (
              sorted(graph.neighbors(i))
              if is_rx
              else list(graph.neighbors(i))
          )
          degree = len(neighbours)
  
          n_terms = [[qml.PauliX(get_nvalue(i))]] + [
              [qml.Identity(get_nvalue(n)), qml.PauliZ(get_nvalue(n))]
              for n in neighbours
          ]
          n_coeffs = [[1, sign] for n in neighbours]
  
          final_terms = [
              qml.operation.Tensor(*list(m)).prune()
              for m in itertools.product(*n_terms)
          ]
          final_coeffs = [
              (0.5**degree)
              * functools.reduce(lambda x, y: x * y, list(m), 1)
              for m in itertools.product(*n_coeffs)
          ]
  
          coeffs.extend(final_coeffs)
          terms.extend(final_terms)
  
      return qml.Hamiltonian(coeffs, terms)
  
file_path: pennylane/pennylane/qaoa/mixers.py
imports: import itertools
  import functools
  from typing import Iterable, Union
  import networkx
  import rustworkx
  import pennylane
  from pennylane.wires import Wires
label_desc: Use image node_id 3 for calling a global function with example usage: bit_flip_mixer(graph, b) and returns: qml